nd) above to factorise \( x^{2}+3 x-4 \)

To factorise \( x^{2}+3 x-4 \), we look for two numbers that multiply to \(-4\) (the constant term) and add up to \(3\) (the coefficient of \(x\). The numbers \(4\) and \(-1\) work perfectly since \(4 \times -1 = -4\) and \(4 + (-1) = 3\). Therefore, we can express the quadratic as \( (x + 4)(x - 1) \). Now you can easily check by expanding: \( (x + 4)(x - 1) = x^2 - x + 4x - 4 = x^2 + 3x - 4\), confirming the factorization is correct. Happy factoring!